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How Valid is a Scleral Tonometer?*
ETIOLOGY OF NONPARALYTIC STRABISMUS Second, the genetic facts are to be accounted for in terms of the temporary physiologic or anatomic cause of onset, and not in terms of any undetected physiologic condi-
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tion assumed to be present at the time of examination. 3536 Kresge Building.
REFERENCES
1. Adler, F. H.: Physiology of the Eye: Clinical Application. St. Louis, Mosby, 1959, ed. 3, p. 471. 2. Gesell, A., Ilg, F. L., and Bullis, G. E.: Vision: Its Development in the Infant and Child. New York, Hoeber, 1949, pp. 88-90. 3. Piaget, J., and Inhelder, B.: The Child's Conception of Space. (Translated by F. J. Langdon and J. L. Lunzer.) London, Routledge and Kegan, 1956, p. 6. 4. McLaughlin, S. C.: Increasing the awareness of diplopia in strabismic patients. Am. Orthoptic J., 9:77-88,1959. 5. : The elicitation of fusion in strabismus patients who are aware of diplopia. Am. J. Ophth., 48:148-153 (July pt. II 1959).
H O W VALID IS A SCLERAL T O N O M E T E R ? * RAYMOND E. HOGG, M.D.,
AND MATHEW ALPERN, P H . D .
Ann Arbor, Michigan The diagnosis of glaucoma is at best a most difficult task, tonometry being one of the many adjuncts in the detection of this disease. Any clinical tonometer, regardless of how accurate, must be considered in the light of what it really contributes to the di agnosis and management of glaucoma. The scleral tonometer which was introduced over 10 years ago1 has enjoyed a certain amount of popularity. Its working principles are similar to those of the well known corneal (Schi^tz) tonometer but it does not require conjunctival anesthesia and it can be used with the patients in a semi-reclining posi tion. 2 · 3 Although the scleral tonometer has been used within the past decade studies of its validity are incomplete. Hirsch 4 found that the correlation coefficient between the sec ond and third repetitions of measurements with the scleral tonometer was +0.77 and this gives an indication of how reliable the instrument is. Talcott3 made measurements with both the corneal and scleral tonometer on 23 patients and found a correlation coeffi* From the Department of Ophthalmology, Uni versity of Michigan. Presented at the meeting of the East-Central Section. Ann Arbor. January, 1960.
cient of +0.85 and concluded that this vali dated the instrument. On the other hand Cockburn5 made a study of the scleral as compared to the Schi^tz tonometer on 22 eyes known to have glaucoma and 22 nonglaucomatous controls. The corneal tonom eter quite accurately differentiated these two groups (with only two false positives and one failure) while the scleral tonometer failed to differentiate the two groups and allowed only poor discrimination. Carter 6 also has made a study of the scleral tonometer with regard to theoretical considerations relating to its use but his measurements do not include any thorough analysis of the validity of the instrument. The present study was undertaken to de termine how accurately the scleral tonometer measures the intraocular pressure with re spect to the standard corneal instrument which has been in use for over 50 years. PROCEDURE
Two separate experiments were carried out: 1. Freshly enucleated adult pig eyes were used in the following manner: Each eye was cannulated through the optic nerve6 where-
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RAYMOND E. HOGG AND MATHEW ALPERN
upon alternate aspirations and injections of saline were carried out to insure patency of the needle. The eye was then placed in a slotted lacrimal irrigation cup and its sur roundings packed with excised retrobulbar fat and muscles. The rim of the cup was encircled with nondrying putty to prevent the semifluid fat from shifting during the experiment. The cannula was connected, through polyethylene tubing, to an open tube water manometer. A three-way stop cock was interposed into the system to make possible the controlled variations in intra ocular pressure by means of a reservoir which could be raised and lowered. Each eye was subjected to intraocular pressures of from 25 to 100 cm. of water at increments of five cm. At each pressure level the ocular tension was estimated by first closing the stopcock completely, moistening the eye, applying the Schip'tz and then the Wolfe tonometer according to prescribed procedure. Early in the course of gathering these data, three separate readings were made with the Wolfe instrument (accepted technique), 3 the first being discarded, and the second and third were averaged to achieve the final recording.f This procedure was abandoned when it was noted that a single reading gave essentially the same re sult. The Schätz recordings were made em ploying weights which would allow for scale readings of between three and ten and were transposed to the 1955 calibration scale of the American Academy of Ophthalmology and Otolaryngology. 2. Using the Wolfe and Schätz instru ments, estimates of intraocular pressures in 44 clinic patients (86 eyes) were carried out. In each instance Pontocaine HC1 (0.5 per cent) was instilled and the Schip'tz measure ments were made according to the standard procedure. The patient was then brought to a semireclining posture and asked to fixate t Hirsch found the test-retest coefficient between the first and second tests to be +0.56; between the first and third tests to be +0.49, and between the second and third test to be +0.77.
his opposite hand while the Wolfe tonom eter, used horizontally, was applied to the upper outer quadrant in such a manner that its footplate was four or more mm. from the limbus and between the insertions of the lateral and superior rectus muscles. RESULTS
The results of the above experiment on the 11 pig eyes are summarized in Fig. 1. This figure shows the mean measured pres sure with each instrument for various con trolled pressures. The slope of the straight lines which are drawn through the data can be regarded as indices of the sensitivity of the instruments. The data for the corneal tonometer approached perfect sensitivity reasonably well. The slope of the best fitting straight line is +0.910. This means that on the average, change in the induced intraocu lar pressure of 10 mm. Hg will be detected by this tonometer as a 9.10 mm. Hg change in intraocular pressure. On the other hand
70 MEAN DATA II EYES
y
O
60-
Z
50-
X / "
40
■>- CORNEAL TONOMETER
30oS^f^*SCLERAL
TONOMETER
^ 10-
*S a
/ 20
30
40
50
60
70
INDUCED PRESSURE (Mm Hg)
Fig. 1 (Hogg and Alpern). Mean data of the manometric measurements of 11 pig eyes with the corneal (open circles) and scleral (closed circles) tonometers. The straight lines have been computed by the method of least squares. The slope of the corneal line is 0.91, that of the scleral line is 0.392.
HOW VALID IS SCLERAL TONOMETER?
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TABLE 1 ANALYSIS OF VARIANCE MEAN DATA 11 EYES A. WOLFE
Slope Scatter Deviations Total
S.S. 19,844.16 686.08 13,293.08 33,823.32
Slope Scatter Deviations Total
S.S. 41,833.18 214.11 12,905.95 54,953.24
D.F. 1 14 160 175
M.S. 19,844.16 41.86 83.08 193.27
F. 238.86 0.501
M.S. 41,833.18 19.46 80.66 314.02
F 518.64 0.2412
B. SCHÄTZ
D.F. 1 14 160 175
the scleral tonometer proved to be consider ably less sensitive. In this case the slope of the straight line which best fits the data is merely 0.392. Hence, on the average, a change of induced pressure of 10 mm. Hg within the eye would only be detected by the scleral tonometer as a 3.92 mm. Hg rise in pressure. In order to investigate this matter fur ther, all of the data for a given instrument, from the 11 pig eyes at the 16 different levels of induced pressure were pooled and an analysis of variance carried out. The re sults of this are summarized in Table 1. While in each case the slope is clearly sig nificantly different from zero, the variance due to deviations at any one induced pres sure about the mean at that pressure was larger than the variance due to deviations about the means of the various induced pressures. This suggested the possibility that the observations on the different eyes were not homogeneous. In order to investigate this possibility a separate analysis of variance was carried out taking into account the fact that eleven dif ferent eyes had been measured. The results of this procedure are summarized in Table 2. There is evidence, for both instruments, of significant differences from one experi ment to the next (scleral tonometer F = 32.24, df = 10,165: corneal tonometer F = 2.97, df = 10,165). How can one account for this? One possibility is that there are signifi
cant slope changes from one experiment to the next with each instrument. In order to investigate this one can test for the hetero geneity of slopes. For the corneal tonometer F = 30.78, df = 10,154 and for the scleral tonometer F = 11.03, df = 10,154. Clearly, for each instrument, the slopes do change significantly from experiments on one eye to those on another. Despite the fact that significant hetero geneity between experiments exists with any one instrument, inspection of the variation removed by the common regressions sug gests that the corneal tonometer is much less variable than the scleral tonometer since the common regression removes a much greater percent of the variation with the corneal tonometer than with the scleral tonometer. Similar data have been reported by others5 and there seems little reason for doubting the generality of this conclusion. Since analysis of variance shows that sig nificant heterogeneity exists between experi ments, a comparison of the sensitivity of each instrument by using the mean data of Figure 1 could perhaps be misleading. In order to compare the sensitivity of the two instruments it would be better to determine the slope of the best fitting line for each in strument in each eye examined. The anal ysis of the data in this manner is summa rized in Table 3. Inspection of the data in dicates that the slope of the best fitting line in each case is larger with the corneal to nometer than with the scleral tonometer.
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R A Y M O N D E. H O G G A N D M A T H E W A L P E R N TABLE 2 ANALYSIS OF VARIANCE ON 11 INDIVIDUAL EYES
Individual regression Common regression
A. W O L F E S.S. D.F. 10,444.38 11 1 8,431.30
M.S. 949.49 8,431.30
F. 145.18 1,289.19 30.78
Heterogeneity
2,013.08
10
201.31
Residual
1,006.14
154
6.54
Total within experiments Between experiments
11,450.52 22,372.80
165 10
69.40 2,237.28
32.24
Total variation
33,823.32
175 B. SCHI0TZ D.F. S.S. 43,805.51 11 1 41,830.98
M.S. 3,982.31 41,830.98
F. 222.35 2,335.62
Individual regression Common regression
1,974.53
10
Residual Total within experiment Between experiments
2,757.79 46,563.30 8,389.94
154 165 10
Total variation
54,953.24
175
Heterogeneity
197.453
11.025
17.91 282.20 838.99
2.97
corneal tonometer are significantly higher (p < 0.001) than the slopes of the best fitting straight line of the data from the scleral to nometer. This supports the validity of the deductions made from the data in Figure 1.
The Mann-Whitney U test can be applied to these data without assumptions regarding the distribution of the regression coeffi cients. This analysis shows that the slopes of the best fitting straight lines applied to the
TABLE 3 SLOPES OF INDIVIDUAL EXPERIMENTS ON 11 PIG EYES
Eye
Schlitz
Rank
Wolfe
Rank
1 2 3 4 5 6 7 8 9 10 11
0.690 0.554 0.700 1.20 1.04 0.883 0.964 0.857 1.16 0.856 1.10
12 9 13 22 19 17 18 16 21 15 20
0.102 0.357 0.615 0.374 0.740 0.281 0.679 0.180 0.440 0.507 0.220
1 5 10 6 14 4 11 2 7 8 3
R 2 = 182
n2 = l l n, = l l
U = n,n2 + U = nin 2 +
n,(n, + l) η,Οι, + Ι)
R,=71
-Rj = 1 2 1 + 6 6 - 7 1 = 1 8 7 - 7 1 = 116 - R 2 = 187-182=5
p is less than 0.001 (p = 0.001 when U = 15 when ni = n2 = l l )
HOW VALID IS SCLERAL TONOMETER?
Fig. 2 (Hogg and Alpern). Scat ter plot of measurements on 86 liv ing human eyes showing the rela tion between measurement with corneal tonometer as compared to those with the scleral tonometer. The dotted line shows what relation is to be expected if the two instru ments correlated perfectly.
1.21 X+14.36
CORNEAL TONOMETER
Clearly, in pig eyes, the scleral tonometer is much less sensitive and the individual measurements much more variable than the corneal tonometer. What then, can be said about the application of the instruments to human eyes? To answer this question measurements with both instruments were taken on a se lected sample of clinical patients. Data was obtained on as wide a range of intraocular pressures as possible. Eighty-six eyes were measured with a pressure range, as meas ured with the corneal tonometer, of from 7.0 mm. Hg to 42.1 mm. Hg. The results from this study are plotted in Figure 2. It is clear from inspection of the data that the agreement between the two instruments is never very good. The range of the scleral tonometer in this same sample was only from 15 to 30 mm. Hg and neither of these two extremes differed from one another very much when their intraocular pressures were compared with the corneal tonometer. If the two instruments were perfectly corre lated, the data should all cluster about the dotted line in the graph which has a slope of unity. Actually they cluster around a line with a slope of only 0.21. The eyes which have low values of intraocular pressure as measured with the corneal tonometer all give too high readings with the scleral instru ment. Conversely those which have high val-
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(Mm Hg)
ues of intraocular pressure tend to show much too low values when measured with the scleral tonometer. These results are what one would anticipate in view of the experi ments on pig eyes. There is considerable reduction of sensi tivity of the scleral tonometer as compared to the corneal tonometer. The readings from the two instruments do correlate to some ex tent ; the correlation coefficient r = +0.596 is significantly larger than zero.* However, this is not sufficiently high to validate the scleral tonometer. This can be emphasized by pointing out that only 35.5 percent (that is, r2 = (0.596) 2 ) of the variation in the measurements with this instrument can be attributed to factors which also will produce a variation in intraocular pressure as meas ured by the corneal tonometer. DISCUSSION
A tonometer should furnish data of the highest possible accuracy which may be used with family and personal histories, results of provocative tests, field examinations, tonographic data, and gonioscopic findings to facilitate the diagnosis and to assess the * This is, however, considerably smaller than the value of +0.85 found by Talcott3 on a sample about half as large. The discrepancy may be in part due to sampling differences and/or individual differ ences among instruments.
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RAYMOND E. HOGG AND MATHEW ALPERN
progress of the already diagnosed case of glaucoma. If an inaccurate instrument were to be depended upon, in screening examina tions where tonometry may be solely relied upon for the detection of glaucoma, then the irrevocable changes of glaucoma could con tinue, even with the blessing of the unwit ting user. The scleral instrument lacks sensi tivity particularly in the critical range where tactile tensions lack sufficient discrimination, that is, in the range from 25 to 35 mm. Hg. It is true that the sclera and cornea are nearly similar in consistency and that both contribute to the continuous fibrous enve lope that encloses the essentially noncompressible fluid intraocular content. It would seem logical that a footplate of proper ra dius of curvature might be designed for an instrument which would function by meas uring impressibility of the sclera. This pos sibility meets a serious obstacle, however, when one considers the episcleral tissues. In order to emphasize this, the following experiment was carried out. Successive measurements were made of the intraocular pressure of one pig eye (which was main tained at a constant level of 29 mm. Hg) al ternately with each instrument for 130 trials. The results of this experiment are plotted in Figure 3. It is evident that while the corneal measurements clustered about a horizontal line in a random way, the scleral measurements showed a continual decre
ment as the number of trials increased. Moreover, this decrement in scleral meas urements was associated with an obvious im pression of the footplate and plunger in the episcleral tissue after only the 12th scleral datum. No comparable impression ever ap peared on the cornea even at the very end of the experiment. It is true that these condi tions do not compare in any realistic way to those in which the instrument would ever be used in living eyes. On the other hand, living eyes do show variation in consistency, thickness, and vascularity of the episcleral tissues (as Sugar has already emphasized, in this regard 8 ). Such individual differences should contribute to the variability of the scleral tonometer just as the change in the form of the episcleral tissues contributes to its variability in Figure 3. In addition to these difficulties it should perhaps be pointed out that normal acts of convergence and palpebral spasm in the presence of normally sensitive conjunctiva8 may also contribute to falsely elevated meas urements of intraocular pressure with the scleral tonometer.* CONCLUSIONS
T h e conclusions of this study may most * The use of the Wolfe instrument held horizon tally has inherent one further source of error. Be cause of its excess weight, the dial end tends to exert a torque on the sleeve which increases friction between the sleeve and the shaft.
oco
x
E E Z
16"
x
o
X X
X
12
o
o° coo o 0 X χοχ o x x o x x xx xx Ä 0
xxx x
x x xxx x X
*V x° «fexrt »
CO
z
XX
XX
Id
X
°x/°
χοχο „ o xo X
tr
Id IUl
5 O
XX XXX XX XX
o 4-
29 Mm Hg
o o0 ° o ocoo 0
MANOMETER PRESSURE I
10
20
-1—
30
—i—
40
TRIALS
-1—
50
60
Fig. 3 (Hogg and Alpern). Measurements on one pig eye re peated for 130 trials alternately with the corneal (x) and scleral (open circles) tonometers. The pressure in the eye was maintained constant at 29 mm. Hg.
HOW VALID IS SCLERAL TONOMETER?
properly only be drawn with regard to the single instrument used in these experiments. The possibility exists, that other scleral to nometers would have fared better under such an analysis and that this particular in strument just happened to be a poor meas uring device. While, if this were true, it would be sufficient reason for rejecting use of a device in which insufficient quality con trol in production does not insure that any given instrument will be clinically adequate, there is evidence that the matter is more serious than this. Recently, after these experiments were completed, we became aware of the com pletely independent work of Cockburn5 using another scleral tonometer. He com pared the results with corneal tonometer readings in much the same way as that de scribed in this present work. The results of his work were in complete agreement with those reported here.* There can be little doubt, therefore, that the generality of the conclusions must be considerably extended 6
* Carter also made a few manometric measure ments on pig eyes with essentially the same results.
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over that which would be otherwise permis sible. It seems highly unlikely that the only instruments so far tested manometrically would not differ more widely in their char acteristics if the factors which contribute to their low validity were not basic artefacts in the measuring procedure. SUMMARY
Manometric measurements on eleven pig eyes with corneal (Schi^tz) and scleral (Wolfe) tonometers showed that the latter was much less sensitive and much more variable than the former. Measurements on 86 living human eyes showed that the data from the two instruments are not sufficiently correlated (r = + 0.596) to validate the scleral instrument. The reasons for the dis crepancies in the readings of the two instru ments are discussed. University Hospital. ACKNOWLEDGMENT
We would like to acknowledge the kind assist ance of Prof W. J. Schull in the statistical analysis of the data and of Prof. H. F. Falls and Prof. David F. Bohr for many helpful suggestions.
REFERENCES
1. Wolfe, O. I., and Wolfe, H. L.: Scleral tonometry. J. A. Optom. A., 21:90, 1949. 2. Wick, R. E.: The scleral tonometer: Technique of application, J. A. Optom. A., 25:207, 1953. 3. Talcott, R. E.: A comparison of corneal and scleral tonometry. A. J. Optom., 35 :31, 1958. 4. Hirsch, M. J.: An evaluation of scleral tonometry. A. J. Optom., 32:391, 1955. 5. Cockburn, D. M.: A comparison of scleral and corneal tonometry. Brit. J. Physiol. Optics, 15:227, 1958. (Also Survey Ophth., 4:157,1959.) 6. Carter, J. H.: The principles of tonometry and the Wolfe scleral tonometer. A. J. Optom., 36:595, 1959. 7. Friedenwald, J. S.: Standardization of tonometers: Decennial report, Am. Acad. Ophth., p. 94, 1954. 8. Sugar, H. S.: Comments on evaluation of scleral tonometry by Hirsch, M. J.4 Survey Ophth., 1:46, 1956.
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tion assumed to be present at the time of examination. 3536 Kresge Building.
REFERENCES
1. Adler, F. H.: Physiology of the Eye: Clinical Application. St. Louis, Mosby, 1959, ed. 3, p. 471. 2. Gesell, A., Ilg, F. L., and Bullis, G. E.: Vision: Its Development in the Infant and Child. New York, Hoeber, 1949, pp. 88-90. 3. Piaget, J., and Inhelder, B.: The Child's Conception of Space. (Translated by F. J. Langdon and J. L. Lunzer.) London, Routledge and Kegan, 1956, p. 6. 4. McLaughlin, S. C.: Increasing the awareness of diplopia in strabismic patients. Am. Orthoptic J., 9:77-88,1959. 5. : The elicitation of fusion in strabismus patients who are aware of diplopia. Am. J. Ophth., 48:148-153 (July pt. II 1959).
H O W VALID IS A SCLERAL T O N O M E T E R ? * RAYMOND E. HOGG, M.D.,
AND MATHEW ALPERN, P H . D .
Ann Arbor, Michigan The diagnosis of glaucoma is at best a most difficult task, tonometry being one of the many adjuncts in the detection of this disease. Any clinical tonometer, regardless of how accurate, must be considered in the light of what it really contributes to the di agnosis and management of glaucoma. The scleral tonometer which was introduced over 10 years ago1 has enjoyed a certain amount of popularity. Its working principles are similar to those of the well known corneal (Schi^tz) tonometer but it does not require conjunctival anesthesia and it can be used with the patients in a semi-reclining posi tion. 2 · 3 Although the scleral tonometer has been used within the past decade studies of its validity are incomplete. Hirsch 4 found that the correlation coefficient between the sec ond and third repetitions of measurements with the scleral tonometer was +0.77 and this gives an indication of how reliable the instrument is. Talcott3 made measurements with both the corneal and scleral tonometer on 23 patients and found a correlation coeffi* From the Department of Ophthalmology, Uni versity of Michigan. Presented at the meeting of the East-Central Section. Ann Arbor. January, 1960.
cient of +0.85 and concluded that this vali dated the instrument. On the other hand Cockburn5 made a study of the scleral as compared to the Schi^tz tonometer on 22 eyes known to have glaucoma and 22 nonglaucomatous controls. The corneal tonom eter quite accurately differentiated these two groups (with only two false positives and one failure) while the scleral tonometer failed to differentiate the two groups and allowed only poor discrimination. Carter 6 also has made a study of the scleral tonometer with regard to theoretical considerations relating to its use but his measurements do not include any thorough analysis of the validity of the instrument. The present study was undertaken to de termine how accurately the scleral tonometer measures the intraocular pressure with re spect to the standard corneal instrument which has been in use for over 50 years. PROCEDURE
Two separate experiments were carried out: 1. Freshly enucleated adult pig eyes were used in the following manner: Each eye was cannulated through the optic nerve6 where-
1222/136
RAYMOND E. HOGG AND MATHEW ALPERN
upon alternate aspirations and injections of saline were carried out to insure patency of the needle. The eye was then placed in a slotted lacrimal irrigation cup and its sur roundings packed with excised retrobulbar fat and muscles. The rim of the cup was encircled with nondrying putty to prevent the semifluid fat from shifting during the experiment. The cannula was connected, through polyethylene tubing, to an open tube water manometer. A three-way stop cock was interposed into the system to make possible the controlled variations in intra ocular pressure by means of a reservoir which could be raised and lowered. Each eye was subjected to intraocular pressures of from 25 to 100 cm. of water at increments of five cm. At each pressure level the ocular tension was estimated by first closing the stopcock completely, moistening the eye, applying the Schip'tz and then the Wolfe tonometer according to prescribed procedure. Early in the course of gathering these data, three separate readings were made with the Wolfe instrument (accepted technique), 3 the first being discarded, and the second and third were averaged to achieve the final recording.f This procedure was abandoned when it was noted that a single reading gave essentially the same re sult. The Schätz recordings were made em ploying weights which would allow for scale readings of between three and ten and were transposed to the 1955 calibration scale of the American Academy of Ophthalmology and Otolaryngology. 2. Using the Wolfe and Schätz instru ments, estimates of intraocular pressures in 44 clinic patients (86 eyes) were carried out. In each instance Pontocaine HC1 (0.5 per cent) was instilled and the Schip'tz measure ments were made according to the standard procedure. The patient was then brought to a semireclining posture and asked to fixate t Hirsch found the test-retest coefficient between the first and second tests to be +0.56; between the first and third tests to be +0.49, and between the second and third test to be +0.77.
his opposite hand while the Wolfe tonom eter, used horizontally, was applied to the upper outer quadrant in such a manner that its footplate was four or more mm. from the limbus and between the insertions of the lateral and superior rectus muscles. RESULTS
The results of the above experiment on the 11 pig eyes are summarized in Fig. 1. This figure shows the mean measured pres sure with each instrument for various con trolled pressures. The slope of the straight lines which are drawn through the data can be regarded as indices of the sensitivity of the instruments. The data for the corneal tonometer approached perfect sensitivity reasonably well. The slope of the best fitting straight line is +0.910. This means that on the average, change in the induced intraocu lar pressure of 10 mm. Hg will be detected by this tonometer as a 9.10 mm. Hg change in intraocular pressure. On the other hand
70 MEAN DATA II EYES
y
O
60-
Z
50-
X / "
40
■>- CORNEAL TONOMETER
30oS^f^*SCLERAL
TONOMETER
^ 10-
*S a
/ 20
30
40
50
60
70
INDUCED PRESSURE (Mm Hg)
Fig. 1 (Hogg and Alpern). Mean data of the manometric measurements of 11 pig eyes with the corneal (open circles) and scleral (closed circles) tonometers. The straight lines have been computed by the method of least squares. The slope of the corneal line is 0.91, that of the scleral line is 0.392.
HOW VALID IS SCLERAL TONOMETER?
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TABLE 1 ANALYSIS OF VARIANCE MEAN DATA 11 EYES A. WOLFE
Slope Scatter Deviations Total
S.S. 19,844.16 686.08 13,293.08 33,823.32
Slope Scatter Deviations Total
S.S. 41,833.18 214.11 12,905.95 54,953.24
D.F. 1 14 160 175
M.S. 19,844.16 41.86 83.08 193.27
F. 238.86 0.501
M.S. 41,833.18 19.46 80.66 314.02
F 518.64 0.2412
B. SCHÄTZ
D.F. 1 14 160 175
the scleral tonometer proved to be consider ably less sensitive. In this case the slope of the straight line which best fits the data is merely 0.392. Hence, on the average, a change of induced pressure of 10 mm. Hg within the eye would only be detected by the scleral tonometer as a 3.92 mm. Hg rise in pressure. In order to investigate this matter fur ther, all of the data for a given instrument, from the 11 pig eyes at the 16 different levels of induced pressure were pooled and an analysis of variance carried out. The re sults of this are summarized in Table 1. While in each case the slope is clearly sig nificantly different from zero, the variance due to deviations at any one induced pres sure about the mean at that pressure was larger than the variance due to deviations about the means of the various induced pressures. This suggested the possibility that the observations on the different eyes were not homogeneous. In order to investigate this possibility a separate analysis of variance was carried out taking into account the fact that eleven dif ferent eyes had been measured. The results of this procedure are summarized in Table 2. There is evidence, for both instruments, of significant differences from one experi ment to the next (scleral tonometer F = 32.24, df = 10,165: corneal tonometer F = 2.97, df = 10,165). How can one account for this? One possibility is that there are signifi
cant slope changes from one experiment to the next with each instrument. In order to investigate this one can test for the hetero geneity of slopes. For the corneal tonometer F = 30.78, df = 10,154 and for the scleral tonometer F = 11.03, df = 10,154. Clearly, for each instrument, the slopes do change significantly from experiments on one eye to those on another. Despite the fact that significant hetero geneity between experiments exists with any one instrument, inspection of the variation removed by the common regressions sug gests that the corneal tonometer is much less variable than the scleral tonometer since the common regression removes a much greater percent of the variation with the corneal tonometer than with the scleral tonometer. Similar data have been reported by others5 and there seems little reason for doubting the generality of this conclusion. Since analysis of variance shows that sig nificant heterogeneity exists between experi ments, a comparison of the sensitivity of each instrument by using the mean data of Figure 1 could perhaps be misleading. In order to compare the sensitivity of the two instruments it would be better to determine the slope of the best fitting line for each in strument in each eye examined. The anal ysis of the data in this manner is summa rized in Table 3. Inspection of the data in dicates that the slope of the best fitting line in each case is larger with the corneal to nometer than with the scleral tonometer.
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R A Y M O N D E. H O G G A N D M A T H E W A L P E R N TABLE 2 ANALYSIS OF VARIANCE ON 11 INDIVIDUAL EYES
Individual regression Common regression
A. W O L F E S.S. D.F. 10,444.38 11 1 8,431.30
M.S. 949.49 8,431.30
F. 145.18 1,289.19 30.78
Heterogeneity
2,013.08
10
201.31
Residual
1,006.14
154
6.54
Total within experiments Between experiments
11,450.52 22,372.80
165 10
69.40 2,237.28
32.24
Total variation
33,823.32
175 B. SCHI0TZ D.F. S.S. 43,805.51 11 1 41,830.98
M.S. 3,982.31 41,830.98
F. 222.35 2,335.62
Individual regression Common regression
1,974.53
10
Residual Total within experiment Between experiments
2,757.79 46,563.30 8,389.94
154 165 10
Total variation
54,953.24
175
Heterogeneity
197.453
11.025
17.91 282.20 838.99
2.97
corneal tonometer are significantly higher (p < 0.001) than the slopes of the best fitting straight line of the data from the scleral to nometer. This supports the validity of the deductions made from the data in Figure 1.
The Mann-Whitney U test can be applied to these data without assumptions regarding the distribution of the regression coeffi cients. This analysis shows that the slopes of the best fitting straight lines applied to the
TABLE 3 SLOPES OF INDIVIDUAL EXPERIMENTS ON 11 PIG EYES
Eye
Schlitz
Rank
Wolfe
Rank
1 2 3 4 5 6 7 8 9 10 11
0.690 0.554 0.700 1.20 1.04 0.883 0.964 0.857 1.16 0.856 1.10
12 9 13 22 19 17 18 16 21 15 20
0.102 0.357 0.615 0.374 0.740 0.281 0.679 0.180 0.440 0.507 0.220
1 5 10 6 14 4 11 2 7 8 3
R 2 = 182
n2 = l l n, = l l
U = n,n2 + U = nin 2 +
n,(n, + l) η,Οι, + Ι)
R,=71
-Rj = 1 2 1 + 6 6 - 7 1 = 1 8 7 - 7 1 = 116 - R 2 = 187-182=5
p is less than 0.001 (p = 0.001 when U = 15 when ni = n2 = l l )
HOW VALID IS SCLERAL TONOMETER?
Fig. 2 (Hogg and Alpern). Scat ter plot of measurements on 86 liv ing human eyes showing the rela tion between measurement with corneal tonometer as compared to those with the scleral tonometer. The dotted line shows what relation is to be expected if the two instru ments correlated perfectly.
1.21 X+14.36
CORNEAL TONOMETER
Clearly, in pig eyes, the scleral tonometer is much less sensitive and the individual measurements much more variable than the corneal tonometer. What then, can be said about the application of the instruments to human eyes? To answer this question measurements with both instruments were taken on a se lected sample of clinical patients. Data was obtained on as wide a range of intraocular pressures as possible. Eighty-six eyes were measured with a pressure range, as meas ured with the corneal tonometer, of from 7.0 mm. Hg to 42.1 mm. Hg. The results from this study are plotted in Figure 2. It is clear from inspection of the data that the agreement between the two instruments is never very good. The range of the scleral tonometer in this same sample was only from 15 to 30 mm. Hg and neither of these two extremes differed from one another very much when their intraocular pressures were compared with the corneal tonometer. If the two instruments were perfectly corre lated, the data should all cluster about the dotted line in the graph which has a slope of unity. Actually they cluster around a line with a slope of only 0.21. The eyes which have low values of intraocular pressure as measured with the corneal tonometer all give too high readings with the scleral instru ment. Conversely those which have high val-
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(Mm Hg)
ues of intraocular pressure tend to show much too low values when measured with the scleral tonometer. These results are what one would anticipate in view of the experi ments on pig eyes. There is considerable reduction of sensi tivity of the scleral tonometer as compared to the corneal tonometer. The readings from the two instruments do correlate to some ex tent ; the correlation coefficient r = +0.596 is significantly larger than zero.* However, this is not sufficiently high to validate the scleral tonometer. This can be emphasized by pointing out that only 35.5 percent (that is, r2 = (0.596) 2 ) of the variation in the measurements with this instrument can be attributed to factors which also will produce a variation in intraocular pressure as meas ured by the corneal tonometer. DISCUSSION
A tonometer should furnish data of the highest possible accuracy which may be used with family and personal histories, results of provocative tests, field examinations, tonographic data, and gonioscopic findings to facilitate the diagnosis and to assess the * This is, however, considerably smaller than the value of +0.85 found by Talcott3 on a sample about half as large. The discrepancy may be in part due to sampling differences and/or individual differ ences among instruments.
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RAYMOND E. HOGG AND MATHEW ALPERN
progress of the already diagnosed case of glaucoma. If an inaccurate instrument were to be depended upon, in screening examina tions where tonometry may be solely relied upon for the detection of glaucoma, then the irrevocable changes of glaucoma could con tinue, even with the blessing of the unwit ting user. The scleral instrument lacks sensi tivity particularly in the critical range where tactile tensions lack sufficient discrimination, that is, in the range from 25 to 35 mm. Hg. It is true that the sclera and cornea are nearly similar in consistency and that both contribute to the continuous fibrous enve lope that encloses the essentially noncompressible fluid intraocular content. It would seem logical that a footplate of proper ra dius of curvature might be designed for an instrument which would function by meas uring impressibility of the sclera. This pos sibility meets a serious obstacle, however, when one considers the episcleral tissues. In order to emphasize this, the following experiment was carried out. Successive measurements were made of the intraocular pressure of one pig eye (which was main tained at a constant level of 29 mm. Hg) al ternately with each instrument for 130 trials. The results of this experiment are plotted in Figure 3. It is evident that while the corneal measurements clustered about a horizontal line in a random way, the scleral measurements showed a continual decre
ment as the number of trials increased. Moreover, this decrement in scleral meas urements was associated with an obvious im pression of the footplate and plunger in the episcleral tissue after only the 12th scleral datum. No comparable impression ever ap peared on the cornea even at the very end of the experiment. It is true that these condi tions do not compare in any realistic way to those in which the instrument would ever be used in living eyes. On the other hand, living eyes do show variation in consistency, thickness, and vascularity of the episcleral tissues (as Sugar has already emphasized, in this regard 8 ). Such individual differences should contribute to the variability of the scleral tonometer just as the change in the form of the episcleral tissues contributes to its variability in Figure 3. In addition to these difficulties it should perhaps be pointed out that normal acts of convergence and palpebral spasm in the presence of normally sensitive conjunctiva8 may also contribute to falsely elevated meas urements of intraocular pressure with the scleral tonometer.* CONCLUSIONS
T h e conclusions of this study may most * The use of the Wolfe instrument held horizon tally has inherent one further source of error. Be cause of its excess weight, the dial end tends to exert a torque on the sleeve which increases friction between the sleeve and the shaft.
oco
x
E E Z
16"
x
o
X X
X
12
o
o° coo o 0 X χοχ o x x o x x xx xx Ä 0
xxx x
x x xxx x X
*V x° «fexrt »
CO
z
XX
XX
Id
X
°x/°
χοχο „ o xo X
tr
Id IUl
5 O
XX XXX XX XX
o 4-
29 Mm Hg
o o0 ° o ocoo 0
MANOMETER PRESSURE I
10
20
-1—
30
—i—
40
TRIALS
-1—
50
60
Fig. 3 (Hogg and Alpern). Measurements on one pig eye re peated for 130 trials alternately with the corneal (x) and scleral (open circles) tonometers. The pressure in the eye was maintained constant at 29 mm. Hg.
HOW VALID IS SCLERAL TONOMETER?
properly only be drawn with regard to the single instrument used in these experiments. The possibility exists, that other scleral to nometers would have fared better under such an analysis and that this particular in strument just happened to be a poor meas uring device. While, if this were true, it would be sufficient reason for rejecting use of a device in which insufficient quality con trol in production does not insure that any given instrument will be clinically adequate, there is evidence that the matter is more serious than this. Recently, after these experiments were completed, we became aware of the com pletely independent work of Cockburn5 using another scleral tonometer. He com pared the results with corneal tonometer readings in much the same way as that de scribed in this present work. The results of his work were in complete agreement with those reported here.* There can be little doubt, therefore, that the generality of the conclusions must be considerably extended 6
* Carter also made a few manometric measure ments on pig eyes with essentially the same results.
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over that which would be otherwise permis sible. It seems highly unlikely that the only instruments so far tested manometrically would not differ more widely in their char acteristics if the factors which contribute to their low validity were not basic artefacts in the measuring procedure. SUMMARY
Manometric measurements on eleven pig eyes with corneal (Schi^tz) and scleral (Wolfe) tonometers showed that the latter was much less sensitive and much more variable than the former. Measurements on 86 living human eyes showed that the data from the two instruments are not sufficiently correlated (r = + 0.596) to validate the scleral instrument. The reasons for the dis crepancies in the readings of the two instru ments are discussed. University Hospital. ACKNOWLEDGMENT
We would like to acknowledge the kind assist ance of Prof W. J. Schull in the statistical analysis of the data and of Prof. H. F. Falls and Prof. David F. Bohr for many helpful suggestions.
REFERENCES
1. Wolfe, O. I., and Wolfe, H. L.: Scleral tonometry. J. A. Optom. A., 21:90, 1949. 2. Wick, R. E.: The scleral tonometer: Technique of application, J. A. Optom. A., 25:207, 1953. 3. Talcott, R. E.: A comparison of corneal and scleral tonometry. A. J. Optom., 35 :31, 1958. 4. Hirsch, M. J.: An evaluation of scleral tonometry. A. J. Optom., 32:391, 1955. 5. Cockburn, D. M.: A comparison of scleral and corneal tonometry. Brit. J. Physiol. Optics, 15:227, 1958. (Also Survey Ophth., 4:157,1959.) 6. Carter, J. H.: The principles of tonometry and the Wolfe scleral tonometer. A. J. Optom., 36:595, 1959. 7. Friedenwald, J. S.: Standardization of tonometers: Decennial report, Am. Acad. Ophth., p. 94, 1954. 8. Sugar, H. S.: Comments on evaluation of scleral tonometry by Hirsch, M. J.4 Survey Ophth., 1:46, 1956.